You have a bag with 3 red balls and 4 blue balls. You draw 2 balls without replacement. What is the probability they are different colors?

You have a bag with 3 red balls and 4 blue balls. You draw 2 balls without replacement. What is the probability they are different colors?

Approach: Calculate probability directly or use complementary probability.

P(different) = 1 - P(same) = 1 - [C(3,2) + C(4,2)]/C(7,2) = 1 - (3+6)/21 = 12/21 = 4/7.

Follow-up: What if you draw with replacement?

Key concepts: hypergeometric distribution, combinations.